So, looking at the "Example weapons" table in the Sword & Scoundrel book:

Halberd 3c, 1p/3p ext r4 2h, Hook, Plate Piercing (Swing)

Should the halberd, firstly, not have the "Maille Piercing (Thrust)" property?

As far as I can tell, if built using the rules, it must use one of: spear-head (which would make it throwing, which doesn't make sense), an awl, which would give it maille-piercing, or it would have a blade on the end, in which case you would definitely make the blade double-edged (maybe severely tapered) but definitely tucked (because you certainly wouldn't use the blade part for swinging) and so, again, it would have the maille-piercing property.

Secondly, and this is a point on which I am certainly not as confident, should the halberd really have the "plate-piercing (swing)" property? According to this Lindybeige video https://www.youtube.com/watch?v=GsckeyktMS0 the halberd would not have been used primarily as a swinging weapon, but instead the axe would have been used in a kind of "pull-back" motion after a (spear) thrust which possibly missed. This motivates the fact that on a halberd the axe head is pointed slightly "downwards" along the shaft rather than perpendicular to the shaft. Wikipedia also says

The halberd consists of an axe blade topped with a spike mounted on a long shaft. It always has a hook or thorn on the back side of the axe blade for grappling mounted combatants.[1] It is very similar to certain forms of the voulge in design and usage. The halberd was usually 1.5 to 1.8 metres (5 to 6 feet) long.[2]

Even if the halberd does have the plate piercing property with the hook / thorn part, perhaps it should be made clear the "plate-piercing" only applies to the "piercing swing" damage and not the "cutting swing".

Spear, axe head and beak with extended length should do it. The beak grants plate piercing to itself; and yes, the plate piercing should only apply to the beak swing; I figured that was implied, though quickly scanning through the rules, I don't see it explicitly stated anywhere. Spear only grants throwing if it's the only head, which it isn't in this case, so no throwing the halberd.

GLENDOWERI can call spirits from the vasty deep.HOTSPURWhy, so can I, or so can any man;But will they come when you do call for them?